Question

Assume that each bag contains 5 balls. Bag a contains 2 red and 3 white, while bag b contains 1 red, 1 white, and 3 blue. You randomly select one ball from bag a, note the color, and place the ball in bag b. You then select a ball from bag b at random and make note of its color. What is the probability that both balls are red?

Answer 1

2/15

Explanation:

Firstly, we calculate the probability of picking a red ball from bag A.

P = number of expected outcomes/number of total outcomes.

P(R1) in bag A = 2/5

Now, we take a ball from bag A and place in bag B. If we selected a red ball, the number of balls in bag B now equals = 2 red balls while the total number of balls now equal 6 balls. Now, the probability is :

P(R2) = 2/6 = 1/3.

The total probability P(R) = P(R1) × P(R2) = 2/5 × 1/3 = 2/15